Public Member Functions | List of all members
Robot Class Reference

DH notation robot class. More...

#include <robot.h>

Inheritance diagram for Robot:
Inheritance graph
[legend]

Public Member Functions

virtual ReturnMatrix C (const ColumnVector &qp)
 Joint torque due to centrifugal and Corriolis based on Recursive Newton-Euler formulation. More...
 
virtual void delta_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &dq, const ColumnVector &dqp, const ColumnVector &dqpp, ColumnVector &ltorque, ColumnVector &dtorque)
 Delta torque dynamics. More...
 
virtual void dq_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &dq, ColumnVector &torque, ColumnVector &dtorque)
 Delta torque due to delta joint position. More...
 
virtual void dqp_torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &dqp, ColumnVector &torque, ColumnVector &dtorque)
 Delta torque due to delta joint velocity. More...
 
virtual void dTdqi (Matrix &dRot, ColumnVector &dp, const int i)
 Partial derivative of the robot position (homogeneous transf.) More...
 
virtual ReturnMatrix dTdqi (const int i)
 Partial derivative of the robot position (homogeneous transf.) More...
 
virtual ReturnMatrix G ()
 Joint torque due to gravity based on Recursive Newton-Euler formulation. More...
 
ReturnMatrix inv_kin (const Matrix &Tobj, const int mj=0)
 Overload inv_kin function. More...
 
virtual ReturnMatrix inv_kin (const Matrix &Tobj, const int mj, const int endlink, bool &converge)
 Inverse kinematics solutions. More...
 
virtual ReturnMatrix inv_kin_puma (const Matrix &Tobj, bool &converge)
 Analytic Puma inverse kinematics. More...
 
virtual ReturnMatrix inv_kin_rhino (const Matrix &Tobj, bool &converge)
 Analytic Rhino inverse kinematics. More...
 
virtual ReturnMatrix inv_kin_schilling (const Matrix &Tobj, bool &converge)
 Analytic Schilling inverse kinematics. More...
 
virtual ReturnMatrix jacobian (const int ref=0) const
 Jacobian of mobile links expressed at frame ref. More...
 
virtual ReturnMatrix jacobian (const int endlink, const int ref) const
 Jacobian of mobile links up to endlink expressed at frame ref. More...
 
virtual ReturnMatrix jacobian_dot (const int ref=0) const
 Jacobian derivative of mobile joints expressed at frame ref. More...
 
virtual void kine_pd (Matrix &Rot, ColumnVector &pos, ColumnVector &pos_dot, const int ref) const
 Direct kinematics with velocity. More...
 
 Robot (const int ndof=1)
 Constructor. More...
 
 Robot (const Matrix &initrobot)
 Constructor. More...
 
 Robot (const Matrix &initrobot, const Matrix &initmotor)
 Constructor. More...
 
 Robot (const Robot &x)
 Copy constructor. More...
 
 Robot (const std::string &filename, const std::string &robotName)
 
virtual void robotType_inv_kin ()
 Identify inverse kinematics familly. More...
 
virtual ReturnMatrix torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp)
 Joint torque, without contact force, based on Recursive Newton-Euler formulation. More...
 
virtual ReturnMatrix torque (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp, const ColumnVector &Fext_, const ColumnVector &Next_)
 Joint torque based on Recursive Newton-Euler formulation. More...
 
virtual ReturnMatrix torque_novelocity (const ColumnVector &qpp)
 Joint torque. when joint velocity is 0, based on Recursive Newton-Euler formulation. More...
 
virtual ~Robot ()
 Destructor. More...
 
- Public Member Functions inherited from Robot_basic
ReturnMatrix acceleration (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &tau)
 Joints acceleration without contact force. More...
 
ReturnMatrix acceleration (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &tau, const ColumnVector &Fext, const ColumnVector &Next)
 Joints acceleration. More...
 
ReturnMatrix dtau_dq (const ColumnVector &q, const ColumnVector &qp, const ColumnVector &qpp)
 Sensitivity of the dynamics with respect to $ q $. More...
 
ReturnMatrix dtau_dqp (const ColumnVector &q, const ColumnVector &qp)
 Sensitivity of the dynamics with respect to $\dot{q} $. More...
 
void error (const std::string &msg1) const
 Print the message msg1 on the console. More...
 
int get_available_dof () const
 Counts number of currently non-immobile links. More...
 
int get_available_dof (const int endlink) const
 Counts number of currently non-immobile links up to and including endlink. More...
 
ReturnMatrix get_available_q (void) const
 Return the joint position vector of available (non-immobile) joints. More...
 
ReturnMatrix get_available_q (const int endlink) const
 Return the joint position vector of available (non-immobile) joints up to and including endlink. More...
 
ReturnMatrix get_available_qp (void) const
 Return the joint velocity vector of available (non-immobile) joints. More...
 
ReturnMatrix get_available_qp (const int endlink) const
 Return the joint velocity vector of available (non-immobile) joints up to and including endlink. More...
 
ReturnMatrix get_available_qpp (void) const
 Return the joint acceleration vector of available (non-immobile) joints. More...
 
ReturnMatrix get_available_qpp (const int endlink) const
 Return the joint acceleration vector of available (non-immobile) joints up to and including endlink. More...
 
bool get_DH () const
 Return true if in DH notation, false otherwise. More...
 
int get_dof () const
 Return dof. More...
 
int get_fix () const
 Return fix. More...
 
Real get_q (const int i) const
 
ReturnMatrix get_q (void) const
 Return the joint position vector. More...
 
ReturnMatrix get_qp (void) const
 Return the joint velocity vector. More...
 
ReturnMatrix get_qpp (void) const
 Return the joint acceleration vector. More...
 
ReturnMatrix inertia (const ColumnVector &q)
 Inertia of the manipulator. More...
 
ReturnMatrix inv_kin (const Matrix &Tobj, const int mj, bool &converge)
 
ReturnMatrix jacobian_DLS_inv (const double eps, const double lambda_max, const int ref=0) const
 Inverse Jacobian based on damped least squares inverse. More...
 
void kine (Matrix &Rot, ColumnVector &pos) const
 Direct kinematics at end effector. More...
 
void kine (Matrix &Rot, ColumnVector &pos, const int j) const
 Direct kinematics at end effector. More...
 
ReturnMatrix kine (void) const
 Return the end effector direct kinematics transform matrix. More...
 
ReturnMatrix kine (const int j) const
 Return the frame j direct kinematics transform matrix. More...
 
ReturnMatrix kine_pd (const int ref=0) const
 Direct kinematics with velocity. More...
 
Robot_basicoperator= (const Robot_basic &x)
 Overload = operator. More...
 
 Robot_basic (const int ndof=1, const bool dh_parameter=false, const bool min_inertial_para=false)
 Constructor. More...
 
 Robot_basic (const Matrix &initrobot_motor, const bool dh_parameter=false, const bool min_inertial_para=false)
 Constructor. More...
 
 Robot_basic (const Matrix &initrobot, const Matrix &initmotor, const bool dh_parameter=false, const bool min_inertial_para=false)
 Constructor. More...
 
 Robot_basic (const std::string &filename, const std::string &robotName, const bool dh_parameter=false, const bool min_inertial_para=false)
 
 Robot_basic (const Robot_basic &x)
 Copy constructor. More...
 
void set_q (const ColumnVector &q)
 Set the joint position vector. More...
 
void set_q (const Matrix &q)
 Set the joint position vector. More...
 
void set_q (const Real q, const int i)
 
void set_qp (const ColumnVector &qp)
 Set the joint velocity vector. More...
 
void set_qpp (const ColumnVector &qpp)
 Set the joint acceleration vector. More...
 
virtual ~Robot_basic ()
 Destructor. More...
 

Additional Inherited Members

- Public Attributes inherited from Robot_basic
ColumnVectora
 
ColumnVectorda
 
ColumnVectordf
 
ColumnVectordF
 
ColumnVectordn
 
ColumnVectordN
 
ColumnVectordp
 
ColumnVectordvp
 
ColumnVectordw
 
ColumnVectordwp
 
ColumnVectorf
 
ColumnVectorF
 
ColumnVectorf_nv
 
ColumnVector gravity
 Gravity vector. More...
 
Linklinks
 Pointer on Link cclass. More...
 
ColumnVectorN
 
ColumnVectorn
 
ColumnVectorn_nv
 
ColumnVectorp
 
ColumnVectorpp
 
MatrixR
 Temprary rotation matrix. More...
 
ColumnVectorvp
 
ColumnVectorw
 
ColumnVectorwp
 
ColumnVector z0
 Axis vector at each joint. More...
 

Detailed Description

DH notation robot class.

Definition at line 340 of file robot.h.

Constructor & Destructor Documentation

Robot::Robot ( const int  ndof = 1)

Constructor.

Definition at line 1242 of file robot.cpp.

Robot::Robot ( const Matrix initrobot)

Constructor.

Definition at line 1251 of file robot.cpp.

Robot::Robot ( const Matrix initrobot,
const Matrix initmotor 
)

Constructor.

Definition at line 1260 of file robot.cpp.

Robot::Robot ( const Robot x)

Copy constructor.

Definition at line 1280 of file robot.cpp.

Robot::Robot ( const std::string &  filename,
const std::string &  robotName 
)
virtual Robot::~Robot ( )
inlinevirtual

Destructor.

Definition at line 348 of file robot.h.

Member Function Documentation

ReturnMatrix Robot::C ( const ColumnVector qp)
virtual

Joint torque due to centrifugal and Corriolis based on Recursive Newton-Euler formulation.

Implements Robot_basic.

Definition at line 360 of file dynamics.cpp.

void Robot::delta_torque ( const ColumnVector q,
const ColumnVector qp,
const ColumnVector qpp,
const ColumnVector dq,
const ColumnVector dqp,
const ColumnVector dqpp,
ColumnVector ltorque,
ColumnVector dtorque 
)
virtual

Delta torque dynamics.

This function computes

\[ \delta \tau = D(q) \delta \ddot{q} + S_1(q,\dot{q}) \delta \dot{q} + S_2(q,\dot{q},\ddot{q}) \delta q \]

Murray and Neuman Cite_: Murray86 have developed an efficient recursive linearized Newton-Euler formulation. In order to apply the RNE as presented in let us define the following variables

\[ p_{di} = \frac{\partial p_i}{\partial d_i} = \left [ \begin{array}{ccc} 0 & \sin \alpha_i & \cos \alpha_i \end{array} \right ]^T \]

\[ Q = \left [ \begin{array}{ccc} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right ] \]

Forward Iterations for $i=1, 2, \ldots, n$. Initialize: $\delta \omega_0 = \delta \dot{\omega}_0 = \delta \dot{v}_0 = 0$.

\[ \delta \omega_i = R_i^T \{\delta \omega_{i-1} + \sigma_i [ z_0 \delta \dot{\theta}_i - Q(\omega_{i-1} + \dot{\theta}_i ) \delta \theta_i ] \} \]

\[ \delta \dot{\omega}_i = R_i^T \{ \delta \dot{\omega}_{i-1} + \sigma_i [z_0 \delta \ddot{\theta}_i + \delta \omega_{i-1} \times (z_0 \dot{\theta}_i ) + \omega_{i-1} \times (z_0 \delta \dot{\theta}_i )] - \sigma_i Q [ \omega_{i-1} + z_0 \ddot{\theta}_i + \omega_{i-1} \times (z_0 \dot{\theta}_i )] \delta \theta_i \} \]

\[ \delta \dot{v}_i = R_i^T \{ \delta \dot{v}_{i-1} - \sigma_i Q \dot{v}_{i-1} \delta \theta_i + (1 -\sigma_i) [z_0 \delta \ddot{d}_i + 2 \delta \omega_{i-1} \times (z_0 \dot{d}_i ) + 2 \omega_{i-1} \times (z_0 \delta \dot{d}_i )] \} + \delta \dot{\omega}_i \times p_i + \delta \omega_i \times ( \omega_i \times p_i) + \omega_i \times ( \delta \omega_i \times p_i) + (1 - \sigma_i) (\dot{\omega}_i \times p_{di} + \omega_i \times ( \omega_i \times p_{di}) ) \delta d_i \]

Backward Iterations for $i=n, n-1, \ldots, 1$. Initialize: $\delta f_{n+1} = \delta n_{n+1} = 0$.

\[ \delta \dot{v}_{ci} = \delta v_i + \delta \omega_i \times r_i + \delta \omega_i \times (\omega_i \times r_i) + \omega_i \times (\delta \omega_i \times r_i) \]

\[ \delta F_i = m_i \delta \dot{v}_{ci} \]

\[ \delta N_i = I_{ci} \delta \dot{\omega}_i + \delta \omega_i \times (I_{ci} \omega_i) + \omega_i \times (I_{ci} \delta \omega_i) \]

\[ \delta f_i = R_{i+1} [ \delta f_{i+1} ] + \delta F_{i} + \sigma_{i+1} Q R_{i+1} [ f_{i+1} ] \delta \theta_{i+1} \]

\[ \delta n_i = R_{i+1} [ \delta n_{i+1} ] + \delta N_{i} + p_{i} \times \delta f_{i} + r_{i} \times \delta F_{i} + (1 - \sigma_i) (p_{di} \times f_{i}) \delta d_i + \sigma_{i+1} Q R_{i+1} [ n_{i+1} ] \delta \theta_{i+1} \]

\[ \delta \tau_i = \sigma_i [ \delta n_i^T (R_i^T z_0) - n_i^T (R_i^T Q z_0) \delta \theta_i] + (1 -\sigma_i) [ \delta f_i^T (R_i^T z_0) ] \]

Implements Robot_basic.

Definition at line 65 of file delta_t.cpp.

void Robot::dq_torque ( const ColumnVector q,
const ColumnVector qp,
const ColumnVector qpp,
const ColumnVector dq,
ColumnVector ltorque,
ColumnVector dtorque 
)
virtual

Delta torque due to delta joint position.

This function computes $S_2(q, \dot{q}, \ddot{q})\delta q$. See Robot::delta_torque for equations.

Implements Robot_basic.

Definition at line 65 of file comp_dq.cpp.

void Robot::dqp_torque ( const ColumnVector q,
const ColumnVector qp,
const ColumnVector dqp,
ColumnVector ltorque,
ColumnVector dtorque 
)
virtual

Delta torque due to delta joint velocity.

This function computes $S_1(q, \dot{q}, \ddot{q})\delta \dot{q}$. See Robot::delta_torque for equations.

Implements Robot_basic.

Definition at line 63 of file comp_dqp.cpp.

void Robot::dTdqi ( Matrix dRot,
ColumnVector dp,
const int  i 
)
virtual

Partial derivative of the robot position (homogeneous transf.)

This function computes the partial derivatives:

\[ \frac{\partial{}^0 T_n}{\partial q_i} = {}^0 T_{i-1} Q_i \; {}^{i-1} T_n \]

in standard notation and

\[ \frac{\partial{}^0 T_n}{\partial q_i} = {}^0 T_{i} Q_i \; {}^{i} T_n \]

in modified notation,

with

\[ Q_i = \left [ \begin{array}{cccc} 0 & -1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right ] \]

for a revolute joint and

\[ Q_i = \left [ \begin{array}{cccc} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 \end{array} \right ] \]

for a prismatic joint.

$dRot$ and $dp$ are modified on output.

Implements Robot_basic.

Definition at line 249 of file kinemat.cpp.

ReturnMatrix Robot::dTdqi ( const int  i)
virtual

Partial derivative of the robot position (homogeneous transf.)

See Robot::dTdqi(Matrix & dRot, ColumnVector & dp, const int i) for equations.

Implements Robot_basic.

Definition at line 334 of file kinemat.cpp.

ReturnMatrix Robot::G ( )
virtual

Joint torque due to gravity based on Recursive Newton-Euler formulation.

Implements Robot_basic.

Definition at line 321 of file dynamics.cpp.

ReturnMatrix Robot::inv_kin ( const Matrix Tobj,
const int  mj = 0 
)
virtual

Overload inv_kin function.

Reimplemented from Robot_basic.

Definition at line 218 of file invkine.cpp.

ReturnMatrix Robot::inv_kin ( const Matrix Tobj,
const int  mj,
const int  endlink,
bool &  converge 
)
virtual

Inverse kinematics solutions.

The solution is based on the analytic inverse kinematics if robot type (familly) is Rhino or Puma, otherwise used the numerical algoritm defined in Robot_basic class.

Reimplemented from Robot_basic.

Definition at line 226 of file invkine.cpp.

ReturnMatrix Robot::inv_kin_puma ( const Matrix Tobj,
bool &  converge 
)
virtual

Analytic Puma inverse kinematics.

converge will be false if the desired end effector pose is outside robot range.

Implements Robot_basic.

Definition at line 348 of file invkine.cpp.

ReturnMatrix Robot::inv_kin_rhino ( const Matrix Tobj,
bool &  converge 
)
virtual

Analytic Rhino inverse kinematics.

converge will be false if the desired end effector pose is outside robot range.

Implements Robot_basic.

Definition at line 251 of file invkine.cpp.

ReturnMatrix Robot::inv_kin_schilling ( const Matrix Tobj,
bool &  converge 
)
virtual

Analytic Schilling inverse kinematics.

converge will be false if the desired end effector pose is outside robot range.

Implements Robot_basic.

Definition at line 508 of file invkine.cpp.

virtual ReturnMatrix Robot::jacobian ( const int  ref = 0) const
inlinevirtual

Jacobian of mobile links expressed at frame ref.

Reimplemented from Robot_basic.

Definition at line 357 of file robot.h.

ReturnMatrix Robot::jacobian ( const int  endlink,
const int  ref 
) const
virtual

Jacobian of mobile links up to endlink expressed at frame ref.

The Jacobian expressed in based frame is

\[ ^{0}J(q) = \left[ \begin{array}{cccc} ^{0}J_1(q) & ^{0}J_2(q) & \cdots & ^{0}J_n(q) \\ \end{array} \right] \]

where $^{0}J_i(q)$ is defined by

\[ ^{0}J_i(q) = \begin{array}{cc} \left[ \begin{array}{c} z_i \times ^{i}p_n \\ z_i \\ \end{array} \right] & \textrm{rotoid joint} \end{array} \]

\[ ^{0}J_i(q) = \begin{array}{cc} \left[ \begin{array}{c} z_i \\ 0 \\ \end{array} \right] & \textrm{prismatic joint} \\ \end{array} \]

Expressed in a different frame the Jacobian is obtained by

\[ ^{i}J(q) = \left[ \begin{array}{cc} ^{0}_iR^T & 0 \\ 0 & ^{0}_iR^T \end{array} \right] {^{0}}J(q) \]

Implements Robot_basic.

Definition at line 352 of file kinemat.cpp.

ReturnMatrix Robot::jacobian_dot ( const int  ref = 0) const
virtual

Jacobian derivative of mobile joints expressed at frame ref.

The Jacobian derivative expressed in based frame is

\[ ^{0}\dot{J}(q,\dot{q}) = \left[ \begin{array}{cccc} ^{0}\dot{J}_1(q,\dot{q}) & ^{0}\dot{J}_2(q,\dot{q}) & \cdots & ^{0}\dot{J}_n(q,\dot{q}) \\ \end{array} \right] \]

where $^{0}\dot{J}_i(q,\dot{q})$ is defined by

\[ ^{0}\dot{J}_i(q,\dot{q}) = \begin{array}{cc} \left[ \begin{array}{c} \omega_{i-1} \times z_i \\ \omega_{i-1} \times ^{i-1}p_n + z_i \times ^{i-1}\dot{p}_n \end{array} \right] & \textrm{rotoid joint} \end{array} \]

\[ ^{0}\dot{J}_i(q,\dot{q}) = \begin{array}{cc} \left[ \begin{array}{c} 0 \\ 0 \\ \end{array} \right] & \textrm{prismatic joint} \\ \end{array} \]

Expressed in a different frame the Jacobian derivative is obtained by

\[ ^{i}J(q) = \left[ \begin{array}{cc} ^{0}_iR^T & 0 \\ 0 & ^{0}_iR^T \end{array} \right] {^{0}}J(q) \]

Implements Robot_basic.

Definition at line 449 of file kinemat.cpp.

void Robot::kine_pd ( Matrix Rot,
ColumnVector pos,
ColumnVector pos_dot,
const int  j 
) const
virtual

Direct kinematics with velocity.

Parameters
RotFrame j rotation matrix w.r.t to the base frame.
posFrame j position vector wr.r.t to the base frame.
pos_dotFrame j velocity vector w.r.t to the base frame.
jFrame j. Print an error on the console if j is out of range.

Implements Robot_basic.

Definition at line 219 of file kinemat.cpp.

void Robot::robotType_inv_kin ( )
virtual

Identify inverse kinematics familly.

Identify the inverse kinematics analytic solution based on the similarity of the robot DH parameters and the DH parameters of know robots (ex: Puma, Rhino, ...). The inverse kinematics will be based on a numerical alogorithm if there is no match .

Implements Robot_basic.

Definition at line 1284 of file robot.cpp.

ReturnMatrix Robot::torque ( const ColumnVector q,
const ColumnVector qp,
const ColumnVector qpp 
)
virtual

Joint torque, without contact force, based on Recursive Newton-Euler formulation.

Implements Robot_basic.

Definition at line 135 of file dynamics.cpp.

ReturnMatrix Robot::torque ( const ColumnVector q,
const ColumnVector qp,
const ColumnVector qpp,
const ColumnVector Fext,
const ColumnVector Next 
)
virtual

Joint torque based on Recursive Newton-Euler formulation.

In order to apply the RNE as presented in Murray 86, let us define the following variables (referenced in the $i^{th}$ coordinate frame if applicable):

$\sigma_i$ is the joint type; $\sigma_i = 1$ for a revolute joint and $\sigma_i = 0$ for a prismatic joint.

$ z_0 = \left [ \begin{array}{ccc} 0 & 0 & 1 \end{array} \right ]^T$

$p_i = \left [ \begin{array}{ccc} a_i & d_i \sin \alpha_i & d_i \cos \alpha_i \end{array} \right ]^T$ is the position of the $i^{th}$ with respect to the $i-1^{th}$ frame.

Forward Iterations for $i=1, 2, \ldots, n$. Initialize: $\omega_0 = \dot{\omega}_0 = 0$ and $\dot{v}_0 = - g$.

\[ \omega_i = R_i^T [\omega_{i-1} + \sigma_i z_0 \dot{\theta}_i ] \]

\[ \dot{\omega}_i = R_i^T \{ \dot{\omega}_{i-1} + \sigma_i [z_0 \ddot{\theta}_i + \omega_{i-1} \times (z_0 \dot{\theta}_i )] \} \]

\[ \dot{v}_i = R_i^T \{ \dot{v}_{i-1} + (1 -\sigma_i) [z_0 \ddot{d}_i + 2 \omega_{i-1} \times (z_0 \dot{d}_i )] \} + \dot{\omega}_i \times p_i + \omega_i \times ( \omega_i \times p_i) \]

Backward Iterations for $i=n, n-1, \ldots, 1$. Initialize: $f_{n+1} = n_{n+1} = 0$.

\[ \dot{v}_{ci} = v_i + \omega_i \times r_i + \omega_i \times (\omega_i \times r_i) \]

\[ F_i = m_i \dot{v}_{ci} \]

\[ N_i = I_{ci} \dot{\omega}_i + \omega_i \times (I_{ci} \omega_i) \]

\[ f_i = R_{i+1} [ f_{i+1} ] + F_{i} \]

\[ n_i = R_{i+1} [ n_{i+1} ] + p_{i} \times f_{i} + N_{i} + r_{i} \times F_{i} \]

\[ \tau_i = \sigma_i n_i^T (R_i^T z_0) + (1 - \sigma_i) f_i^T (R_i^T z_0) \]

Implements Robot_basic.

Definition at line 148 of file dynamics.cpp.

ReturnMatrix Robot::torque_novelocity ( const ColumnVector qpp)
virtual

Joint torque. when joint velocity is 0, based on Recursive Newton-Euler formulation.

Implements Robot_basic.

Definition at line 272 of file dynamics.cpp.


The documentation for this class was generated from the following files:


kni
Author(s): Martin Günther
autogenerated on Fri Jun 7 2019 22:06:46